- #1
Brains_Tom
- 6
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Here's the evil question:
Let X~Exponential(alpha). Derive and name the pdf of Y=(alpha)X
Let X~Exponential(alpha). Derive and name the pdf of Y=(alpha)X
The Exponential Distribution is a probability distribution that models the time between events that occur independently at a constant rate. It is often used to model the waiting time for a specific event to occur.
The Exponential Distribution has one parameter, λ (lambda), which represents the rate at which events occur. This parameter determines the shape of the distribution and can take any positive value.
The probability density function (PDF) for the Exponential Distribution is f(x) = λe^-λx, where x is the time between events. This function describes the relative likelihood of observing a specific value for x.
The Exponential Distribution is unique in that it is the only continuous probability distribution that has a constant failure rate. This means that the probability of an event occurring in a specific time interval is independent of the length of the interval.
The Exponential Distribution is commonly used in reliability and survival analysis, as well as in queuing theory and finance. It can also be used to model the time between earthquakes, radioactive decay, and the length of phone calls.